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dtan5457

  • one year ago

If y^-3x=27, compute exactly 7^2x+1

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  1. dan815
    • one year ago
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    y^(-3x)=27, compute exactly 7^(2x)+1?

  2. dtan5457
    • one year ago
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    7^(2x+1)

  3. Jhannybean
    • one year ago
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    So then you need to figure out x and then plug that x-value into \(7^{2x}+1\) ?

  4. dtan5457
    • one year ago
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    the +1 is part of the exponent

  5. dtan5457
    • one year ago
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    and yes i believe so

  6. dan815
    • one year ago
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    infinite solutions

  7. dtan5457
    • one year ago
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    what would be the steps to attempt to solve this though

  8. dan815
    • one year ago
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    |dw:1443998600989:dw|

  9. Jhannybean
    • one year ago
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    OK dan can you help me for a sec

  10. Jhannybean
    • one year ago
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    How do you make the exponent of y positive without putting it over 1

  11. dan815
    • one year ago
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    |dw:1443999336822:dw|

  12. Jhannybean
    • one year ago
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    Ohh!! got it.

  13. Jhannybean
    • one year ago
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    wow that was dumb lol.

  14. freckles
    • one year ago
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    \[\text{If } y^{-3x}=27, \text{ compute exactly } 7^{2x+1} \] Are we given anything else? Like are we given any restrictions on x and y?

  15. dtan5457
    • one year ago
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    no thats all is given

  16. freckles
    • one year ago
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    \[y^{-3x}=27 \\ y^{3x}=\frac{1}{27} \\ y^{3x}=3^{-3} \\ \ln(y^{3x})=\ln(3^{-3}) \\ 3x \ln(y)=\ln(3^{-3}) \\ 3x \ln(y)=-3 \ln(3) \\ \text{ solve for } x \\ \text{ then replace } x \text{ in } 7^{2x+1}\]

  17. freckles
    • one year ago
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    instructions seem weird it seems like it is looking for like a constant value

  18. Jhannybean
    • one year ago
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    \[\frac{1}{y^{3x}} = 27 \]\[ y^{3x} = \frac{1}{27}\]\[\ln(y^{3x}) = \ln\left(\frac{1}{27}\right)\]\[3x\ln(y)=-\ln(27)\]\[\ln(y)=-\frac{\ln(27)}{3x}\]\[e^{\ln(y)} =e^{-\frac{\ln(27)}{3x}}\]\[y=e^{-\frac{\ln(y)}{3x}}\]

  19. Jhannybean
    • one year ago
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    darnit, took me forever to write out in latex :\ bummer

  20. freckles
    • one year ago
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    but as @dan815 said it isn't

  21. dtan5457
    • one year ago
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    its alright ill just skip this question until my teacher can explain it tomorrow

  22. dtan5457
    • one year ago
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    thanks guys

  23. Jhannybean
    • one year ago
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    typo, meant to write \(\ln(27)\) and i wrote \(ln(y)\) lol.

  24. freckles
    • one year ago
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    this is question come from a book @dtan5457

  25. dtan5457
    • one year ago
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    no just a worksheet written by my teacher

  26. freckles
    • one year ago
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    would it be difficult for you to post an attachment of it here?

  27. dtan5457
    • one year ago
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    im not sure about that as my scanner cant be used at the moment but ill probably have a few more questions from it later

  28. freckles
    • one year ago
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    ok

  29. dtan5457
    • one year ago
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    none of the questions are directly similar but its all pre calc and some trig

  30. freckles
    • one year ago
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    this is prettiest I can make it \[7^{\log_y(\frac{y}{9})}\] but I don't know if it matches the directions to "compute exactly"

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